Final answer:
To find the exact length of the curve y = 28x^(3/2), we use the arc length formula and evaluate the integral.
Step-by-step explanation:
To find the exact length of the curve y = 28x^(3/2), we need to use the arc length formula. The formula is given by L = int(a to b) sqrt(1 + (dy/dx)^2) dx, where a and b are the limits of integration. In this case, a = 0 and b = 1.
We first find dy/dx by taking the derivative of y with respect to x. dy/dx = 3sqrt(2)x^(1/2).
Substituting this into the arc length formula and integrating, we get L = int(0 to 1) sqrt(1 + (3sqrt(2)x^(1/2))^2) dx.
Simplifying the expression inside the square root, we have L = int(0 to 1) sqrt(1 + 18x) dx.
Evaluating the integral gives us the exact length of the curve.